This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms. The construction of Galois representations, which play a fundamental role in Wiles' proof of the ShimuraTaniyama conjecture, is given. In addition, the book presents an outline of the proof... more...

This introduction to Shimura varieties covers key topics including non-triviality of arithmetic invariants and special values of L-functions; elliptic curves over complex and p-adic fields; Hecke algebras; elliptic and modular curves over rings and more. more...

The aim of this book is to give a systematic exposition of results in some important cases where p -adic families and p -adic L -functions are studied. We first look at p -adic families in the following cases: general linear groups, symplectic groups and definite unitary groups. We also look at applications of this theory to modularity lifting problems.... more...